Question

find the value of x,y and z from the given parallelogram
please answer me with solution on today​

Answer 1

Your answer is there☝️, bud. Hope it helps:)

Answer 2

$\displaystyle\large\underline{\sf\red{Given}}$

✭ $\displaystyle\sf \angle DCB = 65^{\circ}$

✭ ABCD is a parallelogram

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ The Value of x,y & z?

$\displaystyle\large\underline{\sf\gray{Solution}}$

✪ Opposite Angles of a parallelogram are equal

✪ Adjacent angles of a parallelogram add up to 180°

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

So as per the figure,

➝ $\displaystyle\sf \angle DCB = \angle DAB \:\:\: \{Alt \ Angles\}$

➝ $\displaystyle\sf \angle DAB = 65^{\circ}$

Also,

➝ $\displaystyle\sf \angle DAB = \angle EFG\:\:\:\{Alt \ Angles\}$

➝ $\displaystyle\sf\green{x = 65^{\circ}}$

Then,

➢ $\displaystyle\sf \angle DCB + \angle CBA = 180^{\circ} \:\:\:\{Adjacent \ Angles\}$

➢ $\displaystyle\sf \angle 65^{\circ} + y = 180^{\circ}$

➢ $\displaystyle\sf y = 180^{\circ}-65^{\circ}$

➢ $\displaystyle\sf \orange{y = 115^{\circ}}$

In parallelogram EFGA

➳ $\displaystyle\sf \angle AEF +\angle EFG = 180^{\circ}\:\:\: \{Adjacent \ Angles \}$

➳ $\displaystyle\sf z+65^{\circ}=180^{\circ}$

➳ $\displaystyle\sf z = 180-65$

➳ $\displaystyle\sf \pink{z = 115^{\circ}}$

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